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Uncertainty principle if position is restricted

  1. Aug 18, 2015 #1
    Hi.

    Assume we have a large number of identical boxes of some finite length ##l## and with infinite potential walls. Let's prepare them all in the same momentum eigenstate. Since for eigenstates ##\Delta p=0##, by the uncertainty principle ##\Delta x## should go to infinity. However, since the particles can't leave the boxes, ##l## is an upper limit for ##\Delta x##. How is this possible?
     
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  3. Aug 18, 2015 #2

    Orodruin

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    There are no momentum eigenstates of the situation you are describing. They simply do not belong to the appropriate Hilbert space.
     
  4. Aug 18, 2015 #3
    Ok, but can we choose states such that ##\Delta p## is small enough (I guess not, that's probably why this doesn't work)?
     
  5. Aug 18, 2015 #4

    Demystifier

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    You cannot do that (if other conditions you mentioned are fulfilled).
     
  6. Aug 18, 2015 #5

    Demystifier

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    Exactly!
     
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